A third representation can be constructed for the generator acting
directly on the hierarchy of moments. For a class of discrete-state
stochastic processes, we have obtained an explicit form for such a
generator acting on the moment
hierarchy [1]}, [2]}.
These are the models of stochastic Chemical Reaction Networks (CRNs),
which have been extensively
studied [3]}, [4]}, [5]}, [6]}, [7]}, [8]}
and are of both mathematical and practical interest. The moments of a
probability distribution for a CRN arrange into a lattice with
coordinates \(k\) , where \(k\)  is a vector whose components determine the
moment of interest.
